Fluctuations and criticality in the random-field Ising model

We investigate the critical properties of the d = 3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength h and system sizes V = L x L x L, with L <= 156. Using the sample-to-sample fluctuations of various quantities and proper finite-size scaling techniques we estimate with high accuracy the critical disorder strength h(c) and the correlation length exponent nu. Additional simulations in the area of the estimated critical-field strength and relevant scaling analysis of the bond energy suggest bounds for the specific heat critical exponent alpha and the violation of the hyperscaling exponent theta. Finally, a data collapse analysis of the order parameter and disconnected susceptibility provides accurate estimates for the critical exponent ratios beta/nu and (gamma) over bar/nu, respectively. DOI: 10.1103/PhysRevE.87.032119